The Department of Labor reported today that the unemployment rate fell to 7.8 percent in September, and the number of people reporting they have jobs rose by a surprisingly high 873,000.

And within nanoseconds, there was political controversy. Specifically, former GE CEO Jack Welch tweeted this: @jack_welch “Unbelievable jobs numbers..these Chicago guys will do anything..can't debate so change numbers”

And then conservative pundits piled on, with multiple accusations that the numbers are too good to be true and must have been influenced or manipulated by the White House for political gain after the president’s poor debate performance.

The office of Secretary of Labor Hilda Solis offered this statement: “I’m insulted when I hear accusations of any foul play because we have a very professional civil service organization with the top economists working at the Bureau of Labor Statistics. These are the best trained and most-skilled analysts, and it’s really ludicrous to hear that kind of statement.”

But could a manipulation of the data — for political or other reasons — actually happen?

Here’s how the monthly unemployment numbers in the Department of Labor’s household survey are compiled. The Census Bureau surveys about 60,000 representative households, asking how many adults are working and unemployed. They hand the numbers off to career civil servants at the Bureau of Labor Statistics, who crunch them to get the unemployment rate, the number of people currently employed, and other statistics.

“Numbers can be manipulated,” says Paul Conway, who was chief of staff to Secretary of Labor Elaine Chao under President George W. Bush. Conway now runs a conservative advocacy group, Generation Opportunity, trying to galvanize the youth vote. “They [BLS staff] produce a product, that is then subject to the review, and approval and processing of political appointees in the department. That’s a fact—that’s exactly how it works before anything goes public.”

Conway says political appointees didn’t change the numbers when he was at the Department of Labor. But he says of today’s report: “I find it at best incredible, and at worst suspicious.”

John Galvin is acting commissioner at the Bureau of Labor Statistics, and he says the president, his council of economic advisers, and the Labor Secretary’s staff do see the report before the rest of us. It’s delivered — according to Office of Management and Budget regulations — to the president and his advisors the day before, and the Secretary of Labor half-an-hour before, release.

“The numbers are locked up, and the press release is going to print by the afternoon of the day before,” Galvin says, “so there can’t be any further change after that point.”

How about the data-crunching? Could those 60,000 households that are surveyed by Census workers be skewed Democrat? Or could the number of people working and unemployed, or the labor force participation rate, be fudged by BLS staff?

Gary Burtless of the Brookings Institution worked as a senior economist in the Department of Labor — civil service, not political appointee — in both the Carter and Reagan Administrations.

“There are a lot of steps between when the raw data are collected and we end up with estimates of the unemployment rate, where either mistakes or purposeful manipulation could affect things,” says Burtless. “But the people in the Bureau of Labor Statistics are much more loyal to their professional duties than they are to the person who happens to be holding office at the time, and who may not be there in six month’s time.”

Douglas Holtz-Eakin served in the Council of Economic Advisors under George W. Bush. He says there’s no possibility this report was manipulated or changed for political ends. But he says the household survey is volatile and unreliable month-to-month.

“It can’t be right,” says Holtz-Eakin. “It’s not consistent with any of the other economic data that we have. And what is very likely to happen is that next month, they will walk door-to-door to a better representative sample of American households, and they’ll find a lot fewer people are employed.”